# Problem: A clever engineer designs a "sprong" that obeys the force law Fx=-q(x-xe)3, where xe is the equilibrium position of the end of the sprong and q is the sprong constant. For simplicity, well let xe=0. Then Fx=-qx3.Find an expression for the potential energy of a stretched or compressed sprong.A sprong-loaded toy gun shoots a 21 g plastic ball. What is the launch speed if the sprong constant is 4.3×104 N/m3 and the sprong is compressed 13 cm ? Assume the barrel is frictionless.What are the units of q?

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###### Problem Details

A clever engineer designs a "sprong" that obeys the force law Fx=-q(x-xe)3, where xe is the equilibrium position of the end of the sprong and q is the sprong constant. For simplicity, well let xe=0. Then Fx=-qx3.

Find an expression for the potential energy of a stretched or compressed sprong.

A sprong-loaded toy gun shoots a 21 g plastic ball. What is the launch speed if the sprong constant is 4.3×104 N/m3 and the sprong is compressed 13 cm ? Assume the barrel is frictionless.

What are the units of q?